COOPERATIVE MANAGEMENT LETTER
MARCH 2010 | CML 10-02
Getting More
From Your Numbers
Dr. John Park
Roy B. Davis Professor of
Agricultural Cooperation
Reading and interpreting numerical information is part of running a
successful business. Processing a lot of numbers to discover their underlying story can be an overwhelming task. Here are some tips to
ease your number anxieties.
M
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y father was my first and greatest teacher. An agricultural
economist himself, he influenced the way that I view the world
around me. He often told me “figures
don’t lie, but liars can sure figure” as a
way to remind me that the numbers and
reported statistics we read often have
more than one interpretation.
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Numbers are a means of giving voice to
abstract concepts. In this sense they are
an integral part of our business language. We use them to communicate
progress, performance, levels, and values. In business, they are often the
means for determining a course of
action.
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Cooperative Management Letter
is funded through the Roy B. Davis
Professorship in Agricultural Cooperation at Texas A&M University.
© 2010
Department of Agricultural Economics
Texas A&M University
2124 TAMU
College Station, TX 77843-2124
Phone: (979) 845-1751
Email: jlpark@tamu.edu
http://cooperatives.tamu.edu/
without understanding the message
that lies beneath. This can lead to misinterpretation of the message followed
by poor decision-making. Whether examining financial statements or a survey
of members, a basic understanding of
numerical data and the
ways in which they are presented can help avoid such
pitfalls.
This requires processing hundreds of
variables representing costs, revenues,
interest rates, production levels, and
more. Unfortunately, tracking all these
variables and the ways they relate to
one another all at once is simply beyond human ability.
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Data Types
We refer to a collection of information
and numerical statistics as data. There
are two important aspects of data that
impact the way we examine them. One
is in regard to the type of data and the
other is in regard to the way they are
summarized.
Instead, we summarize data using
key indicators that will produce a desired
result. Thus, we focus on concepts that
utilize averages, totals, differences, and
rates. Open any financial statement and
you will see them: operating income,
operating expense, net margins, debt
service, depreciation, taxes, liquidity,
profitability, turnover, and more.
Data are either quantitative (numerical) or qualitative (categorical) in nature. Quantitative data can be measured
and placed in order. Their values
have meaning, and thus comparisons and ratios have meaning. On
the other hand, qualitative data like
gender, marital status, or yes/no
questions help us to categorize information. Sometimes we represent this information with numbers, but unless
the responses have a meaningful order comparisons
and ratios have little meaning.
Herein lies our problem; we can be
overly focused on the summary data
For example, if we survey gin
managers about their operations, we
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COOPERATIVE MANAGEMENT LETTER could ask about the manager’s salary (quantitative data)
and whether or not the cooperative provides his vehicle
(qualitative data). Both of these things used together give
us a more complete picture of the manager’s compensation.
As previously mentioned, data are often summarized to
help us focus on specific concepts. Some of these data
focus on a single variable and are simple representations
of the variable over time or aggregated for a group of
people (like average manager salary). Others require calculations involving more than one variable (like net margin). This small difference becomes important when we
try to interpret the message behind these numbers.
Statistics 101
One of the first things a researcher might do when sharing data is to present a snapshot of the dataset to give the
audience a basis for interpretation. This is often done using mean, median, mode, and range.
The mean is what you might normally associate with the
term “average”. If we have the salaries of 5 cooperative
managers, we add them together and divide by 5. However, there are two other ways of looking at the “average”
of the data.
The median is found by placing all the responses in numerical order and choosing the one in the middle (the
third highest value in our previous example). This is the
middle response, which has no regard for the relative
magnitude of the responses.
The mode is found by identifying the most frequently
occurring response. It is useful when talking about qualitative or categorical data.
The range is simply the difference between the largest
value in the data and the smallest.
Thus, mean, median, and mode give us an idea of the
center or average of the data, and the range gives us an
idea of how close the numbers are to one another. See the
example on this page for a demonstration of these concepts.
When reporting this survey we could say that the average
manager is paid $50,000 per year. However, that is only
one way of looking at things. Using another measure of
average we could say that the manager in the middle of
the data is paid $55,000 per year, or that more managers
are paid $30,000 per year more than any other amount.
MARCH 2010 | CML 10-02
An Example of Descriptive Statistics
Respondent
Manager 1
Manager 2
Manager 3
Manager 4
Manager 5
Mean
Median
Mode
Range
What is your
salary?
$55,000
$70,000
$65,000
$30,000
$30,000
Does the co-op
provide a truck?
Yes
No
No
Yes
Yes
$50,000
$55,000
$30,000
$40,000
N/A
N/A
“Yes”
N/A
Calculations:
Mean:
(55,000 + 70,000 + 65,000 + 30,000 + 30,000) ÷ 5 = 50,000
Median:
Placing the responses in order of their value (30,000, 30,000,
55,000, 65,000, 70,000) shows us that the value in the exact
middle (the 3rd out of 5) = 55,000
Mode:
Two of the respondents indicated a salary of 30,000, making it
the most common response.
Range:
Simply take the difference of the highest and lowest values.
70,000 - 30,000 = 40,000
Consider this:
• If you were told that the average manager made $50,000,
would this tell the whole story?
• How does the additional information of a truck allowance impact your interpretation of the salary data?
• How well does the average represent the entire group?
• Is there any inherent bias in these numbers? Do you have reasons to believe that they are a fair representation of all cooperative managers?
As you can see, the way that the data are summarized can
skew our vision of what is actually contained in the data.
A Very Important Question
Finally, when looking at data, whether it comes from surveys or financial statements, there is one very important
question to ask yourself before interpreting results: where
does this number come from? Once you understand how a
number is calculated, you can make decisions on what it
means and how to affect its value in the future if needed.
Educational programs of Texas AgriLife Extension are open to all people without regard to race, color, sex, disability, religion, age, or national origin.
Issued in furtherance of Cooperative Extension Work in Agriculture and Home Economics, Acts of Congress of May 8, 1914, as amended, and June 30, 1914, in cooperation
with the United States Department of Agriculture, Edward G. Smith, Director, Texas AgriLife Extension Service, The Texas A&M University System.